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Mathematics
Problem
Prove that
∫
0
a
f
(
x
)
d
x
=
∫
0
a
f
(
a
−
x
)
⋅
d
x
\int_{0}^{a} f(x) dx = \int_{0}^{a} f(a-x) \cdot dx
∫
0
a
f
(
x
)
d
x
=
∫
0
a
f
(
a
−
x
)
⋅
d
x
and hence Evaluate
∫
0
a
x
x
+
a
−
x
d
x
\int_{0}^{a} \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a-x}} dx
∫
0
a
x
+
a
−
x
x
d
x
(J-19) a. Prove that
∫
0
a
f
(
x
)
d
x
=
∫
0
a
f
(
a
−
x
)
⋅
d
x
\int_{0}^{a} f(x) dx = \int_{0}^{a} f(a-x) \cdot dx
∫
0
a
f
(
x
)
d
x
=
∫
0
a
f
(
a
−
x
)
⋅
d
x
b. Evaluate
∫
0
a
x
x
+
a
−
x
d
x
\int_{0}^{a} \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a-x}} dx
∫
0
a
x
+
a
−
x
x
d
x
(J-19)
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